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New insights into the distribution of the topmost gap in random walks and Lévy flights
Claude Godrèche, Jean-Marc Luck · 2025-02-26 · via math.PR updates on arXiv.org

Building upon the knowledge of the distribution of the first positive position reached by a random walker starting from the origin, one can derive new results on the statistics of the gap between the largest and second-largest positions of the walk, and recover known ones in a more direct manner.

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